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(4+x^4)*atan(x^1+4/x)/x^3

  • ¿Cómo usar?

  • Derivada de:
  • Derivada de x=3at/1+t^2
  • Derivada de x*10^x Derivada de x*10^x
  • Derivada de (tgx+4)' Derivada de (tgx+4)'
  • Derivada de (t^2+5*t-1)/t^2 Derivada de (t^2+5*t-1)/t^2

  • Expresiones idénticas

  • (cuatro +x^ cuatro)*atan(x^ uno + cuatro /x)/x^ tres
  • (4 más x en el grado 4) multiplicar por arco tangente de gente de (x en el grado 1 más 4 dividir por x) dividir por x al cubo
  • (cuatro más x en el grado cuatro) multiplicar por arco tangente de gente de (x en el grado uno más cuatro dividir por x) dividir por x en el grado tres
  • (4+x4)*atan(x1+4/x)/x3
  • 4+x4*atanx1+4/x/x3
  • (4+x⁴)*atan(x^1+4/x)/x³
  • (4+x en el grado 4)*atan(x en el grado 1+4/x)/x en el grado 3
  • (4+x^4)atan(x^1+4/x)/x^3
  • (4+x4)atan(x1+4/x)/x3
  • 4+x4atanx1+4/x/x3
  • 4+x^4atanx^1+4/x/x^3
  • (4+x^4)*atan(x^1+4 dividir por x) dividir por x^3

  • Expresiones semejantes

  • (4+x^4)*atan(x^1-4/x)/x^3
  • (4-x^4)*atan(x^1+4/x)/x^3
  • (4+x^4)*arctan(x^1+4/x)/x^3
Derivada de la función/ (4+x^4)*atan(x^1+4/x)/x^3

Derivada de (4+x^4)*atan(x^1+4/x)/x^3

Función f() - derivada -er orden en el punto
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
/     4\     / 1   4\
\4 + x /*atan|x  + -|
             \     x/
---------------------
           3         
          x
(x4+4)atan⁡(x1+4x)x3\frac{\left(x^{4} + 4\right) \operatorname{atan}{\left(x^{1} + \frac{4}{x} \right)}}{x^{3}} 
((4 + x^4)*atan(x^1 + 4/x))/x^3
Gráfica
02468-8-6-4-2-1010-500000500000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                    /    4 \ /     4\                          
                    |1 - --|*\4 + x /                          
                    |     2|                                   
   3     / 1   4\   \    x /                                   
4*x *atan|x  + -| + -----------------                          
         \     x/                 2                            
                          / 1   4\        /     4\     / 1   4\
                      1 + |x  + -|      3*\4 + x /*atan|x  + -|
                          \     x/                     \     x/
------------------------------------- - -----------------------
                   3                                4          
                  x                                x
4x3atan⁡(x1+4x)+(1−4x2)(x4+4)(x1+4x)2+1x3−3(x4+4)atan⁡(x1+4x)x4\frac{4 x^{3} \operatorname{atan}{\left(x^{1} + \frac{4}{x} \right)} + \frac{\left(1 - \frac{4}{x^{2}}\right) \left(x^{4} + 4\right)}{\left(x^{1} + \frac{4}{x}\right)^{2} + 1}}{x^{3}} - \frac{3 \left(x^{4} + 4\right) \operatorname{atan}{\left(x^{1} + \frac{4}{x} \right)}}{x^{4}}
Simplificar
Segunda derivada [src] 
  /                                                                         /               2        \                                         \
  |    /                   /    4 \ /     4\\                               |       /    4 \  /    4\|                                         |
  |    |                   |1 - --|*\4 + x /|                               |       |1 - --| *|x + -||                                         |
  |    |                   |     2|         |                               |       |     2|  \    x/|                                         |
  |    |   3     /    4\   \    x /         |                      /     4\ |  4    \    x /         |                                         |
  |  3*|4*x *atan|x + -| + -----------------|                      \4 + x /*|- -- + -----------------|                                         |
  |    |         \    x/                 2  |                               |   3                 2  |      3 /    4 \                         |
  |    |                          /    4\   |                               |  x           /    4\   |   4*x *|1 - --|     /     4\     /    4\|
  |    |                      1 + |x + -|   |                               |          1 + |x + -|   |        |     2|   6*\4 + x /*atan|x + -||
  |    \                          \    x/   /      2     /    4\            \              \    x/   /        \    x /                  \    x/|
2*|- ---------------------------------------- + 6*x *atan|x + -| - ----------------------------------- + ------------- + ----------------------|
  |                     x                                \    x/                          2                          2              2          |
  |                                                                                /    4\                    /    4\              x           |
  |                                                                            1 + |x + -|                1 + |x + -|                          |
  \                                                                                \    x/                    \    x/                          /
------------------------------------------------------------------------------------------------------------------------------------------------
                                                                        3                                                                       
                                                                       x
2(4x3(1−4x2)(x+4x)2+1+6x2atan⁡(x+4x)−(x4+4)((1−4x2)2(x+4x)(x+4x)2+1−4x3)(x+4x)2+1−3(4x3atan⁡(x+4x)+(1−4x2)(x4+4)(x+4x)2+1)x+6(x4+4)atan⁡(x+4x)x2)x3\frac{2 \left(\frac{4 x^{3} \left(1 - \frac{4}{x^{2}}\right)}{\left(x + \frac{4}{x}\right)^{2} + 1} + 6 x^{2} \operatorname{atan}{\left(x + \frac{4}{x} \right)} - \frac{\left(x^{4} + 4\right) \left(\frac{\left(1 - \frac{4}{x^{2}}\right)^{2} \left(x + \frac{4}{x}\right)}{\left(x + \frac{4}{x}\right)^{2} + 1} - \frac{4}{x^{3}}\right)}{\left(x + \frac{4}{x}\right)^{2} + 1} - \frac{3 \left(4 x^{3} \operatorname{atan}{\left(x + \frac{4}{x} \right)} + \frac{\left(1 - \frac{4}{x^{2}}\right) \left(x^{4} + 4\right)}{\left(x + \frac{4}{x}\right)^{2} + 1}\right)}{x} + \frac{6 \left(x^{4} + 4\right) \operatorname{atan}{\left(x + \frac{4}{x} \right)}}{x^{2}}\right)}{x^{3}}
Simplificar
Tercera derivada [src] 
  /    /                            /               2        \                \                                                                                                                                                                                                                         \
  |    |                            |       /    4 \  /    4\|                |                                                                                                                                                                                                                         |
  |    |                            |       |1 - --| *|x + -||                |                                                                                                                                                                                                                         |
  |    |                            |       |     2|  \    x/|                |                                                                                                                                                                                                                         |
  |    |                   /     4\ |  4    \    x /         |                |                                                                           /              3               3        2                      \                                                                              |
  |    |                   \4 + x /*|- -- + -----------------|                |                                                                           |      /    4 \        /    4 \  /    4\       /    4 \ /    4\|                                   /               2        \                 |
  |    |                            |   3                 2  |      3 /    4 \|                         /                   /    4 \ /     4\\            |      |1 - --|      4*|1 - --| *|x + -|    24*|1 - --|*|x + -||                                   |       /    4 \  /    4\|                 |
  |    |                            |  x           /    4\   |   4*x *|1 - --||                         |                   |1 - --|*\4 + x /|            |      |     2|        |     2|  \    x/       |     2| \    x/|                                   |       |1 - --| *|x + -||                 |
  |    |                            |          1 + |x + -|   |        |     2||                         |                   |     2|         |   /     4\ |12    \    x /        \    x /                \    x /        |                                   |       |     2|  \    x/|                 |
  |    |   2     /    4\            \              \    x/   /        \    x /|                         |   3     /    4\   \    x /         |   \4 + x /*|-- + ------------ - -------------------- + -------------------|                                 3 |  4    \    x /         |                 |
  |  9*|6*x *atan|x + -| - ----------------------------------- + -------------|                      18*|4*x *atan|x + -| + -----------------|            | 4              2                   2          /           2\ |                             12*x *|- -- + -----------------|                 |
  |    |         \    x/                          2                          2|                         |         \    x/                 2  |            |x        /    4\      /           2\         3 |    /    4\ | |                                   |   3                 2  |       2 /    4 \|
  |    |                                   /    4\                    /    4\ |                         |                          /    4\   |            |     1 + |x + -|      |    /    4\ |        x *|1 + |x + -| | |      /     4\     /    4\         |  x           /    4\   |   18*x *|1 - --||
  |    |                               1 + |x + -|                1 + |x + -| |                         |                      1 + |x + -|   |            |         \    x/      |1 + |x + -| |           \    \    x/ / |   30*\4 + x /*atan|x + -|         |          1 + |x + -|   |         |     2||
  |    \                                   \    x/                    \    x/ /            /    4\      \                          \    x/   /            \                      \    \    x/ /                          /                   \    x/         \              \    x/   /         \    x /|
2*|- -------------------------------------------------------------------------- + 12*x*atan|x + -| + ----------------------------------------- - ------------------------------------------------------------------------- - ----------------------- - -------------------------------- + --------------|
  |                                      x                                                 \    x/                        2                                                                2                                             3                                  2                         2 |
  |                                                                                                                      x                                                          /    4\                                             x                            /    4\                   /    4\  |
  |                                                                                                                                                                             1 + |x + -|                                                                      1 + |x + -|               1 + |x + -|  |
  \                                                                                                                                                                                 \    x/                                                                          \    x/                   \    x/  /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                     3                                                                                                                                                   
                                                                                                                                                    x
2(−12x3((1−4x2)2(x+4x)(x+4x)2+1−4x3)(x+4x)2+1+18x2(1−4x2)(x+4x)2+1+12xatan⁡(x+4x)−(x4+4)(−4(1−4x2)3(x+4x)2((x+4x)2+1)2+(1−4x2)3(x+4x)2+1+24(1−4x2)(x+4x)x3((x+4x)2+1)+12x4)(x+4x)2+1−9(4x3(1−4x2)(x+4x)2+1+6x2atan⁡(x+4x)−(x4+4)((1−4x2)2(x+4x)(x+4x)2+1−4x3)(x+4x)2+1)x+18(4x3atan⁡(x+4x)+(1−4x2)(x4+4)(x+4x)2+1)x2−30(x4+4)atan⁡(x+4x)x3)x3\frac{2 \left(- \frac{12 x^{3} \left(\frac{\left(1 - \frac{4}{x^{2}}\right)^{2} \left(x + \frac{4}{x}\right)}{\left(x + \frac{4}{x}\right)^{2} + 1} - \frac{4}{x^{3}}\right)}{\left(x + \frac{4}{x}\right)^{2} + 1} + \frac{18 x^{2} \left(1 - \frac{4}{x^{2}}\right)}{\left(x + \frac{4}{x}\right)^{2} + 1} + 12 x \operatorname{atan}{\left(x + \frac{4}{x} \right)} - \frac{\left(x^{4} + 4\right) \left(- \frac{4 \left(1 - \frac{4}{x^{2}}\right)^{3} \left(x + \frac{4}{x}\right)^{2}}{\left(\left(x + \frac{4}{x}\right)^{2} + 1\right)^{2}} + \frac{\left(1 - \frac{4}{x^{2}}\right)^{3}}{\left(x + \frac{4}{x}\right)^{2} + 1} + \frac{24 \left(1 - \frac{4}{x^{2}}\right) \left(x + \frac{4}{x}\right)}{x^{3} \left(\left(x + \frac{4}{x}\right)^{2} + 1\right)} + \frac{12}{x^{4}}\right)}{\left(x + \frac{4}{x}\right)^{2} + 1} - \frac{9 \left(\frac{4 x^{3} \left(1 - \frac{4}{x^{2}}\right)}{\left(x + \frac{4}{x}\right)^{2} + 1} + 6 x^{2} \operatorname{atan}{\left(x + \frac{4}{x} \right)} - \frac{\left(x^{4} + 4\right) \left(\frac{\left(1 - \frac{4}{x^{2}}\right)^{2} \left(x + \frac{4}{x}\right)}{\left(x + \frac{4}{x}\right)^{2} + 1} - \frac{4}{x^{3}}\right)}{\left(x + \frac{4}{x}\right)^{2} + 1}\right)}{x} + \frac{18 \left(4 x^{3} \operatorname{atan}{\left(x + \frac{4}{x} \right)} + \frac{\left(1 - \frac{4}{x^{2}}\right) \left(x^{4} + 4\right)}{\left(x + \frac{4}{x}\right)^{2} + 1}\right)}{x^{2}} - \frac{30 \left(x^{4} + 4\right) \operatorname{atan}{\left(x + \frac{4}{x} \right)}}{x^{3}}\right)}{x^{3}}
Simplificar
Gráfico
Derivada de (4+x^4)*atan(x^1+4/x)/x^3
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